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Simplicity of Beliefs and Delay Tactics in a Concession Game

Authors

Ran Spiegler

Disciplines

Philosophy

Abstract

Simplicity of beliefs and delay tactics in a concession game Simplicity of Beliefs and Delay Tactics in a Concession Game Ran Spiegler∗ School of Economics Tel Aviv University Tel Aviv 69978, Israel February 19, 2003 Abstract I explore the idea of simplicity as a belief-selection criterion in games. A pair of strategies in finite-automata representation (s1, s2) is a “Simple Nash Equilibrium” (SINE) if: (1) sj is a best-reply to si ; (2) every automaton for player j, which generates the same path as sj (given si), has at least as many states as sj . I apply SINE to a bilateral concession game and show that it captures an aspect of bargaining behavior: players employ delay tactics in order to justify their concessions. Delay tactics are mutually reinforcing, and this may prevent players from reaching an interior agreement. ∗I am deeply grateful to the Institute for Advanced Study at Princeton for its stimulat- ing hospitality. I also thank Eddie Dekel, Kfir Eliaz, Michele Piccione, Ariel Rubinstein, an associate editor and a referee for helpful comments. 1 1 Introduction The idea that complexity considerations may affect players’ choice of strategy has become entrenched in the game-theoretic literature, following Rubinstein (1986), Abreu and Rubinstein (1988), Banks and Sundaram (1990), Piccione (1992), Chatterjee and Sabourian (2000) and others. The assumption un- derlying these works is that complex strategies are more costly to implement than simple strategies. By comparison, the analogous idea of complexity as a criterion for belief selection in games has been virtually unexplored. Preference for simple the- ories is of course an ancient philosophical notion. Usually it is applied to the exalted realm of scientific inquiry, but there is no reason why it should not be relevant to the more mundane business of playing games. One way to implement this idea in the context of two-person games is to assume that among the entire set of beliefs that are consistent with a

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